Permutation Table (nPr Chart) Calculator

Enter a maximum n to generate a table of permutation values nPr for every n and r. Computed exactly with BigInt.

Input

Enter a maximum n to display a table of permutation nPr values for varying n and r.

Maximum n

Enter an integer from 0 to 15.

Largest value (8P8)

40,320

Permutation nPr table

Rows are n, columns are r, and each cell is the value of nPr.

n / r	r = 0	r = 1	r = 2	r = 3	r = 4	r = 5	r = 6	r = 7	r = 8
n = 0	1	0	0	0	0	0	0	0	0
n = 1	1	1	0	0	0	0	0	0	0
n = 2	1	2	2	0	0	0	0	0	0
n = 3	1	3	6	6	0	0	0	0	0
n = 4	1	4	12	24	24	0	0	0	0
n = 5	1	5	20	60	120	120	0	0	0
n = 6	1	6	30	120	360	720	720	0	0
n = 7	1	7	42	210	840	2,520	5,040	5,040	0
n = 8	1	8	56	336	1,680	6,720	20,160	40,320	40,320

Diagonal (r = n)

nPn equals n factorial

nPr = n × (n − 1) × … × (n − r + 1) = n! ÷ (n − r)!. It is 1 when r is 0 and 0 when r exceeds n.

The permutation nPr is the number of ways to arrange r items chosen from n distinct items in order, given by nPr = n × (n − 1) × … × (n − r + 1).
An equivalent form is nPr = n! ÷ (n − r)!, where n! is the factorial of n.
When r is 0, nPr = 1, and when r is greater than n, nPr = 0. The diagonal of the table where r = n equals n!.
This tool uses BigInt to return exact integer values without overflow. A maximum n limit keeps the table from growing too large.

Tell us what you think of this calculator.